Zanarkand Ruins : Go along the linear path for a bit. There will be a familiar scene as you progress to the next area.

Zanarkand Ruins: Overpass: Save after that scene and follow the party to the Overpass. Go along the path for a while; as you go around the left bend, look for the Fortune Sphere chest. In the next area, there will be a scene. As you go along the linear path thereafter, look for a small "lump" on the minimap where you can find a Spiritual Targe. Continue along.

Dome : Save and enter.

Dome: Interior : Go along the path for a bit, descending ever-deeper. As you go beneath an overpass and just past it, go east and along the path there heading back the way you came along the overpass; you’ll get 10,000 Gil at the end. Return to the ground and follow the path for a while more to a Save Sphere. Continue walking on past there to a fork. If you go east, you’ll find a Friend Sphere . Grab it, then go along the other branch. As you go along, a bunch of spirits will pass by. At that point, look for a southwestbound path on the other side of the bridge at the end of which you’ll find a Lv. 3 Key Sphere. Return to the main path and keep going.

Dome: Corridor : As you go along the hall here, stick along the right side and you can get a Luck Sphere . Continue up to the Save Sphere, then into the Cloister.